Several Guaranteed Descent Conjugate Gradient Methods for Unconstrained Optimization

Abstract

This paper investigates a general form of guaranteed descent conjugate gradient methods which satisfies the descent condition $g_k^T{d}_k\le -\left(\mathrm{1}-\mathrm{1}/\left(\mathrm{4}{\theta }_k\right)\right){∥g_k∥}^2\hspace{0.17em}\hspace{0.17em}\left({\theta }_k>\mathrm{1}/\mathrm{4}\right)$ and which is strongly convergent whenever the weak Wolfe line search is fulfilled. Moreover, we present several specific guaranteed descent conjugate gradient methods and give their numerical results for large-scale unconstrained optimization.